Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
774 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #24910304 | C2 | semidirect |
| 2. #24908300 | C2 | semidirect |
| 3. #24907407 | C2 | semidirect |
| 4. #24905979 | C2 | semidirect |
| 5. #24905368 | C2 | semidirect |
| 6. #24905348 | C2 | semidirect |
| 22. C2×AGL(1,ℤ/8)×C83 | C4 | semidirect |
| 27. #417×C83 | C4 | semidirect |
| 155. Q8×C83 | #99 | semidirect |
| 245. C83 | #9368 | semidirect |
| 247. C2×AGL(1,ℤ/8) | Dic83 | semidirect |
| 254. #417 | Dic83 | semidirect |
| 393. Q8 | #14581707 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24910304 | 2 |
| #24908300 | 2 |
| #24907407 | 2 |
| #24905979 | 2 |
| #24905368 | 2 |
| #24905348 | 2 |
| C83×#3006 | 2 |
| #9368 | 83 |